Paper Info
Title
A numerical approach to design control invariant sets for constrained nonlinear discrete-time systems with guaranteed optimality
Abstract
A numerical approach to design control invariant sets for constrained nonlinear discrete-time systems with guaranteed optimality is proposed in this paper. The addressed approach is based on the fact that zonotopes are more flexible for representing sets than boxes in interval analysis. Then the solver of set inversion via interval analysis is extended to set inversion via zonotope geometry by introducing the novel idea of bisecting zonotopes. The main feature of the extended solver of set inversion is the bisection and the evolution of a zonotope rather than a box. Thus the shape of admissible domains for set inversion can be broadened from boxes to zonotopes and the wrapping effect can be reduced as well by using the zonotope evolution instead of the interval evolution. Combined with global optimization via interval analysis, the extended solver of set inversion via zonotope geometry is further applied to design control invariant sets for constrained nonlinear discrete-time systems in a numerical way. Finally, the numerical design of a control invariant set and its application to the terminal control of the dual-mode model predictive control are fulfilled on a benchmark Continuous-Stirred Tank Reactor example.
Year
DOI
Venue
2009
10.1007/s10898-008-9334-6
J. Global Optimization
Keywords
Field
DocType
Set inversion,Global optimization,Interval analysis,Zonotope geometry,Control invariant sets
Mathematical optimization,Nonlinear system,Global optimization,Model predictive control,Invariant (mathematics),Solver,Set inversion,Discrete time and continuous time,Interval arithmetic,Mathematics
Journal
Volume
Issue
ISSN
44
3
0925-5001
Citations 
PageRank 
References 
4
0.41
15
Authors
3
Name
Order
Citations
PageRank
Jian Wan140.41
Josep Vehi261.13
Ningsu Luo3257.78